The standard theorem for stochastic matrices with positive entries is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the positivity condition is replaced by a condition on the distances between columns.
American Mathematical Monthly
Required Publisher's Statement
Published by The Mathematical Association of America
Ćurgus, Branko and Jewett, Robert I., "Somewhat Stochastic Matrices" (2015). Mathematics. 61.